Recent content by IB1

Homework Statement You are arguing over a cell phone while trailing an unmarked police car by 25.0 m; both your car and the police car are traveling at 110 km/h. Your argument diverts your attention from the police car for 2.0 s (long enough for you to look at the phone and yell,“I won't do...

Hi. Well, it's not a homework problem, that's for sure. I haven't done much progress on this problem, seems quite hard. Or perhaps just my elementary geometry skills suck ? I've tried to somehow interpret this geometric problem in complex numbers' language, you know, but didn't really work as I...

Let PQRS be a rectangle inscribed in a triangle ABC(i.e P is in AC, Q in BC and R,S are in AB). Find the locus of points that are intersection of diagonals of the rectangle. (i.e find the locus of intersection of RQ and PS)

Well, I can understand that distributivity might not hold for "some sets and some operations" ... but still it's written + and . and so the operations are addition and multiplication ... I could understand if it were written like this [c#(a*b)=c#a*c#b] ? So, Mark44, are you suggesting that when...

Yes, but why then in the begging of the chapter we develop arithmetic on rings if + and . are simply addition and multiplication? Moreover, the third axiom [ c(a+b)=ca +cb, (a+b)c=ac+bc] would be trivial and we wouldn't need to check for it ever because it is always true. Sorry for bombing...

I need to learn some abstract algebra, and it's pretty hard doing this on my own. Please help me. According to the definition, Ring is an algebraic structure with two binary operations , commonly called addition (+) and multiplication ( . ). We write (R,+, .). Some examples of rings are: (Z, +...

Homework Statement 1. A long pendulum has time period 10s. If the bob is displaced 2m from the equilibrum position and released, how long will it take to move 1m ? 2. As a mass on a spring travels upwards through the equilibrium position, its velocity is 0.5m/s. If the frequency of the...

Radium decays emitting alpha particles into Radon. i) Explain, in terms of momentum of the particles, why the radon nucleus and the alpha particles move off in opposite directions after the reaction. ii) The speed of the radon nucleus after the reaction is v_{R} and that of the alpha...

@rs1n: Can you post/direct your proof of General Mean Inequality using induction. Personally, I am aware of only one proof for it, it is simply using the fact that: f(n)=\left(\frac{a_1 ^n +a_2 ^n +...+a_n ^n}{n}\right)^{1/n} is increasing function, for a_i being positive.

As for finding the cubic root of 64, you have to solve equation x^3=64

There are Algebraic Methods. But I simply do not recommend them to you or to anyone else. Is far much simpler to know Euler's Function, or even some elementary abstract algebra knowledge would do the work. If you want to learn these methods to use them in Mathematical Olympiads, then I prefer...

Indeed, Euler's Totient Function is a very nice generalization of Fermat's Little Theorem. There is an intuitive proof for both which is studied in "Olympiad Training" but if you're a student, you may try to use group properties. (hint- consider the set {1,2,...,p-1} and the multiplication...

Yeah this is only AM-GM for four numbers, but you can also use Holder's inequality or Jensen's inequality. In fact, AM-GM inequality is just a corollary of Jensen's inequality (hint- for proof consider the function f(x)=ln x). As for AM-GM inequality, it is: If a_i , i=1,2,...,n are positive...

Thank you both for your fast replies. I understood.

A train of mass m=1.5 \cdot 10^5 kg is traveling at 40m/s when the brakes are applied and it decelerates steadily. The train travels a distance of 250m before coming to a halt. a) Calculate the deceleration of the train. b) Find the average braking force. I have tried to solve...